Isomers of Alkanes
After studying C6H14, we became interested in the structure of carbon hydrogen compounds in general. I discovered, later, that molecules that are made up of only carbon and hydrogen atoms that contain no cycles are called alkanes. Isomers are compounds that have the same number of carbon and hydrogen atoms, but have different structures. Since hydrogen atoms do not add to the basic structure of alkanes, it is sufficient to study the underlying structure of the carbon atoms.
In connection to graph theory, studying the structure of the carbon atoms in alkane isomers is equivalent to studying the structure of nonisomorphic trees with no vertex of degree greater than four. The following graphs (representing trees, or the structure of carbon atoms in alkanes) are grouped vertically by the number of vertices.
The result that we began to notice while comparing the groups of isomers was that the beginning of a Fibonacci sequence appeared: 1, 1, 2, 3, 5.
Seeing that this pattern was developing, we tried to think of a reason why. But once I tested C7H16, the pattern fell apart. Instead of finding 8 isomers, as a Fibonacci sequence would produce, there are 9 (see below).